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Supply and Demand (from the GRE Economics Test) In the market for soybeans, the demand and supply functions are \(Q_{D}=100-10 P\) and \(Q_{S}=20+5 P\), where \(Q_{D}\) is quantity demanded, \(Q_{S}\) is quantity supplied, and \(P\) is price in dollars. If the government sets a price floor of \(\$ 7\), what will be the resulting surplus or shortage?

Short Answer

Expert verified
At the price floor of $7, the quantity demanded for soybeans is 30 and the quantity supplied is 55. To find the surplus or shortage, we calculate the difference between these values: \(Q_S - Q_D = 55 - 30 = 25\). Since the result is positive, there is a surplus of 25 units of soybeans at the price floor of $7.

Step by step solution

01

Determine the quantity demanded and supplied at the price floor

At the given price floor, P = 7. We will substitute this value into the demand and supply functions to determine the quantity demanded and supplied at this price. For \(Q_D\), we have: \(Q_D = 100 - 10P = 100 - 10(7) = 100 - 70 = 30\). For \(Q_S\), we have: \(Q_S = 20 + 5P = 20 + 5(7) = 20 + 35 = 55\). So at the price floor of $7, the quantity demanded is 30 and the quantity supplied is 55.
02

Calculate the surplus or shortage

Now that we have the quantity demanded and supplied, we can find the surplus or shortage by finding the difference between \(Q_S\) and \(Q_D\): Surplus or Shortage = \(Q_S - Q_D = 55 - 30 = 25\). Since the result is positive, there is a surplus of 25 units of soybeans at the price floor of $7.

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Key Concepts

These are the key concepts you need to understand to accurately answer the question.

Supply and Demand
When we talk about supply and demand, we're referring to the fundamental economic concept that explains how prices are determined in a market. The law of supply and demand states that the price of a good or service is determined by the quantity of that good or service that is available (supply) and the desire of buyers to purchase it (demand).

When the amount of a product that consumers want to buy (quantity demanded) equals the amount that producers want to sell (quantity supplied), the market is said to be in equilibrium. The corresponding price is the equilibrium price. However, when there is an imbalance, such as a government-imposed price floor, the market can't reach equilibrium. A price floor is a minimum price set by the government, and it can result in a surplus (where the quantity supplied exceeds the quantity demanded) or a shortage (where the quantity demanded exceeds the quantity supplied).
Quantity Demanded
The quantity demanded is the total number of units of a good or service that consumers are willing and able to purchase at a given price over a specified period of time. It is an important concept in economics because it helps us understand consumer preferences and purchasing behavior.

The quantity demanded is inversely related to price, which is described by the law of demand: as prices rise, the quantity demanded tends to fall, and vice versa. This relationship can be graphically represented with a downward-sloping demand curve on a price-quantity graph. However, the quantity demanded can change due to factors other than price, such as changes in income, tastes, or the prices of other related goods.
Quantity Supplied
Conversely, the quantity supplied represents the amount of a particular good or service that producers are willing and able to sell at a certain price level at a given moment. The relationship between price and quantity supplied is direct, as captured by the law of supply: higher prices incentivize producers to supply more of a good or service, and lower prices discourage production.

This quantity supplied can be graphically depicted by an upward-sloping supply curve on the same type of price-quantity graph that is used for demand. Markets thrive on the balance between quantity demanded and quantity supplied, but external interventions like price floors can disrupt this balance, often leading to excess supply or even shortages.
Economics
The branch of knowledge concerned with the production, consumption, and transfer of wealth is known as economics. It studies how individuals, businesses, governments, and nations make choices on allocating resources to satisfy their wants and needs. Economics can be divided into microeconomics, which focuses on the behavior of individual consumers and firms, and macroeconomics, which looks at the economy as a whole.

Understanding the mechanisms of economics such as supply, demand, and governmental policies like price controls is critical for predicting market behaviors and making informed decisions. In the context of this exercise, analyzing the effects of a price floor on the market for soybeans has allowed us to explore how economic principles predict a surplus, which can have significant real-world consequences.

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Most popular questions from this chapter

In the \(1990 \mathrm{~s}\), significant numbers of tourists traveled from North America and Asia to Australia and South Africa. In 1998 , a total of \(2,230,000\) of these tourists visited Australia, while 390,000 of them visited South Africa. Also, 630,000 of these tourists came from North America, and a total of \(2,620,000\) tourists traveled from these two regions to these two destinations. \(^{22}\) (Assume no single tourist visited both destinations or traveled from both North America and Asia.) a. The given information is not sufficient to determine the number of tourists from each region to each destination. Why? b. If you were given the additional information that a total of \(1,990,000\) tourists came from Asia, would you now be able to determine the number of tourists from each region to each destination? If so, what are these numbers? c. If you were given the additional information that 200,000 tourists visited South Africa from Asia, would you now be able to determine the number of tourists from each region to each destination? If so, what are these numbers?

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